Although many hand-crafted choices for \( R \)  exist, such as tgv [1]} or wavelet-based approaches [2]}, it is generally agreed upon that modeling higher order image statistics should be based on learning [3]}.
In contrast to the widely adopted feed-forward approaches, in this work we retain the variational structure to allow statistical interpretation.
To account for the parameters, we extend (REF ) to
\(E(x, f, \phi ) D(x, f) + R(x, \phi ),\) 
